Diffusion weighted imaging (DWI) is a widely used magnetic resonance (MR) modality for noninvasive diagnostics. One example diffusion quantity that clinical practitioners will measure is mean diffusivity, which is useful because it indirectly reflects tissue cellularity via water mobility and is independent of the relative orientation between the applied diffusion gradient directions and directional tissue cytoarchitecture. Mean diffusivity is commonly referred to as “apparent diffusion coefficient” (ADC) and may be determined from a variety of tissue/media-based models of how diffusion weighted MRI (DWI) signal changes with applied diffusion gradient strength. See, e.g., Riches et al., Diffusion-weighted imaging of the prostate and rectal wall: comparison of biexponential and monoexponential modelled diffusion and associated perfusion coefficients. NMR Biomed 2009; 22(3): 318-325; Lemke A, et al. Toward an optimal distribution of b values for intravoxel incoherent motion imaging. Magn Reson Imaging 2011; 29(6):766-776. Sensitivity to diffusion phenomena is controlled by a “b-value” which is derived from the full temporal DWI gradient waveform.
Absolute apparent diffusion coefficient (ADC) has been suggested as a potential biomarker for cancer diagnosis and treatment monitoring. See, Chenevert et al., Diffusion magnetic resonance imaging: an early surrogate marker of therapeutic efficacy in brain tumors. Journal of the National Cancer Institute 2000; 92:2029-2036; Padhani et al. Diffusion-weighted magnetic resonance imaging as a cancer biomarker: consensus and recommendations. Neoplasia 2009; 11:102-125.). To detect clinically significant changes in diffusion measurements, the sources of technical variability have to be well-characterized separately from biological changes. System designers desire to understand variations in results caused by equipment and testing conditions, to better control for such variations when measuring biological changes. The desire is heightened because for applications to be useful in clinical environment synchronization and standardization of diffusion measurement methodology among and across multiple MRI platforms is needed, otherwise multi-institutional studies and widespread clinical utilization can be hampered.
A significant platform-dependent variation has been identified as a source of spatial-dependent error in ADC measurement. Such errors have been demonstrated on commercial MRI equipment by using a temperature-controlled (ice water) phantom for a precisely known diffusion fluid. Chenevert et al., Diffusion coefficient measurement using temperature controlled fluid for quality control in multi-center studies. J Magn Reson Imag 2011; 34:983-987, and Chenevert et al., Multi-system repeatability and reproducibility of apparent diffusion coefficient measurement using an ice-water phantom” JMRI 2012. The testing showed that gradient non-linearity was the primary source of the error leading to a spatially-dependent b-value and subsequent ADC bias that can exceed 10-20% over clinically relevant FOVs on some systems. This platform-dependent bias results in spatial non-uniformity errors that substantially deteriorate quantitative DWI measurements.
The early accounts of DWI errors related to gradient non-linearity are now a decade old, see, Robson, Non-linear Gradients on Clinical MRI Systems Introduce Systematic Errors in ADC and DTI Measurements. In Proceedings of the 10th Annual Meeting of ISMRM, Honolulu, Hi., USA, 2002. p. 912), but the systematic bias problem has clearly persisted for contemporary clinical systems. This is presumably due to lack of practical correction procedures for vendor implementation for wide-scale non-research applications.
Previous research on non-linearity correction (see, Bammer et al., Analysis and generalized correction of the effect of spatial gradient field distortions in diffusion weighted imaging. Magn Reson Med 2003; 50:560-569 U.S. Pat. No. 6,969,991 and Janke et al., Use of Spherical Harmonic Deconvolution Methods to Compensate for Nonlinear Gradient Effects on MRI Images Magn Reson Med 2004; 52:115-122) described approaches for correction of diffusion tensor imaging (DTI) that required full spatial-mapping of the gradient coil fields as well as measuring of at least 6 non-collinear DWI gradient directions in each experiment. This comprehensive approach accounted for both direction and magnitude errors in diffusion tensor due to gradient nonlinearity, although the underlying mathematical algorithm is known to be susceptible to measurement noise (Laun et al., How background noise shifts eigenvectors and increases eigenvalues in DTI. Magn Reson Mater Phy 2009; 22:151-158). Furthermore, sampling of many directions, as required for DTI, prolongs image acquisition beyond the desired scantime for most clinical applications, where only a measure of mean diffusivity is sought. To streamline correction for background and imaging gradient errors in DTI, a simplified empiric DWI calibration algorithm was introduced (Wu et al., A Method for Calibrating Diffusion Gradients in Diffusion Tensor Imaging. J Comput Assist Tomogr. 2007; 31: 984-993) based on a regression model, without reference to the system's hardware characteristics. The approach was dependent upon gradient waveforms and did not generalize well to different scanner types and tissue properties. Others have incorporated the interaction of imaging gradients with diffusion gradients in their model (Ozcan A. Characterization of Imaging Gradients in Diffusion Tensor Imaging. J Magn Reson 2010; 207:24-33.), but failed to account for gradient nonlinearity and cross-terms. In short, the purported corrective techniques suggested thus far, whether for DTI, DWI, or otherwise, have not been successful in practical implementation of simultaneous corrections for gradient nonlinearity and cross terms corrupting mean diffusivity MRI measurement.
There is a desire to perform imaging using the fewest number of directional measurements that allow quantitation of mean diffusivity. In the absence of gradient nonlinearity, three orthogonal gradient directions would be adequate. However, as surmised by Bammer, gradient nonlinearity required solution via acquisition of at least six directions (much longer scantime) to derive three diffusion tensor characteristics from which mean diffusivity was calculated.